For Dressing: Whisk together the first 6 ingredients in a bowl. Gradually whisk in oil. (Dressing can be made 1 day ahead. Cover and chill.)
For Rice: In a large heavy sauce pan, bring 4 cups of water to boil. Add rice, salt and bay leaves and stir well. Cover and reduce heart to low. Cook until water is absorbed, about 20 minutes. Remove bay leaves. Transfer rice to a large bowl.
Add dressing and oregano and toss well. Cover and refrigerate until cool, about 2 hours. (Can be prepared 1 day ahead). When ready to serve, mix in pine nuts, capers and chives into rice. Season with salt and pepper and serve.